The 31-year-old world number 28 ended Fognini's 13-match winning streak with an emphatic 6-0 6-3 triumph in 62 minutes of clay-court action.
Fifth-seeded Robredo lost just six points in the first set - only one on serve - as he built a commanding lead.
Fognini, who was chasing a third successive tournament win, broke to lead 2-1 early in the second but any hopes of a fightback were soon quashed.
Robredo's success followed his victory at the Grand Prix Hassan II tournament in Casablanca in April, which had been his first trophy in two years.
After being beset by injury last season, the former world number five has risen from a lowly ranking of 118 at the start of this year and showed determination to climb further.
Despite the defeat Fognini, on the back of his tournament wins in Stuttgart and Hamburg this month, is poised to move to a new career-high of around 16.